#region Using

using System;
using System.Runtime.Serialization;

#endregion

namespace DotNetMatrix {
	/// <summary>Eigenvalues and eigenvectors of a real matrix. 
	/// If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
	/// diagonal and the eigenvector matrix V is orthogonal.
	/// I.e. A = V.Multiply(D.Multiply(V.Transpose())) and 
	/// V.Multiply(V.Transpose()) equals the identity matrix.
	/// If A is not symmetric, then the eigenvalue matrix D is block diagonal
	/// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
	/// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].  The
	/// columns of V represent the eigenvectors in the sense that A*V = V*D,
	/// i.e. A.Multiply(V) equals V.Multiply(D).  The matrix V may be badly
	/// conditioned, or even singular, so the validity of the equation
	/// A = V*D*Inverse(V) depends upon V.cond().
	/// 
	/// </summary>
	[Serializable]
	public class EigenvalueDecomposition : ISerializable {
		#region	 Class variables

		/// <summary>Array for internal storage of nonsymmetric Hessenberg form.
		/// @serial internal storage of nonsymmetric Hessenberg form.
		/// </summary>
		private double[][] H;

		/// <summary>Array for internal storage of eigenvectors.
		/// @serial internal storage of eigenvectors.
		/// </summary>
		private double[][] V;

		/// <summary>Arrays for internal storage of eigenvalues.
		/// @serial internal storage of eigenvalues.
		/// </summary>
		private double[] d, e;

		/// <summary>Symmetry flag.
		/// @serial internal symmetry flag.
		/// </summary>
		private bool issymmetric;

		/// <summary>Row and column dimension (square matrix).
		/// @serial matrix dimension.
		/// </summary>
		private int n;

		/// <summary>Working storage for nonsymmetric algorithm.
		/// @serial working storage for nonsymmetric algorithm.
		/// </summary>
		private double[] ort;

		#endregion //  Class variables

		#region Private Methods

		// Symmetric Householder reduction to tridiagonal form.

		[NonSerialized] private double cdivi;
		[NonSerialized] private double cdivr;

		private void tred2() {
			//  This is derived from the Algol procedures tred2 by
			//  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
			//  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
			//  Fortran subroutine in EISPACK.

			for(int j = 0; j < n; j++) {
				d[j] = V[n - 1][j];
			}

			// Householder reduction to tridiagonal form.

			for(int i = n - 1; i > 0; i--) {
				// Scale to avoid under/overflow.

				double scale = 0.0;
				double h = 0.0;
				for(int k = 0; k < i; k++) {
					scale = scale + Math.Abs(d[k]);
				}
				if(scale == 0.0) {
					e[i] = d[i - 1];
					for(int j = 0; j < i; j++) {
						d[j] = V[i - 1][j];
						V[i][j] = 0.0;
						V[j][i] = 0.0;
					}
				} else {
					// Generate Householder vector.

					for(int k = 0; k < i; k++) {
						d[k] /= scale;
						h += d[k]*d[k];
					}
					double f = d[i - 1];
					double g = Math.Sqrt(h);
					if(f > 0) {
						g = - g;
					}
					e[i] = scale*g;
					h = h - f*g;
					d[i - 1] = f - g;
					for(int j = 0; j < i; j++) {
						e[j] = 0.0;
					}

					// Apply similarity transformation to remaining columns.

					for(int j = 0; j < i; j++) {
						f = d[j];
						V[j][i] = f;
						g = e[j] + V[j][j]*f;
						for(int k = j + 1; k <= i - 1; k++) {
							g += V[k][j]*d[k];
							e[k] += V[k][j]*f;
						}
						e[j] = g;
					}
					f = 0.0;
					for(int j = 0; j < i; j++) {
						e[j] /= h;
						f += e[j]*d[j];
					}
					double hh = f/(h + h);
					for(int j = 0; j < i; j++) {
						e[j] -= hh*d[j];
					}
					for(int j = 0; j < i; j++) {
						f = d[j];
						g = e[j];
						for(int k = j; k <= i - 1; k++) {
							V[k][j] -= (f*e[k] + g*d[k]);
						}
						d[j] = V[i - 1][j];
						V[i][j] = 0.0;
					}
				}
				d[i] = h;
			}

			// Accumulate transformations.

			for(int i = 0; i < n - 1; i++) {
				V[n - 1][i] = V[i][i];
				V[i][i] = 1.0;
				double h = d[i + 1];
				if(h != 0.0) {
					for(int k = 0; k <= i; k++) {
						d[k] = V[k][i + 1]/h;
					}
					for(int j = 0; j <= i; j++) {
						double g = 0.0;
						for(int k = 0; k <= i; k++) {
							g += V[k][i + 1]*V[k][j];
						}
						for(int k = 0; k <= i; k++) {
							V[k][j] -= g*d[k];
						}
					}
				}
				for(int k = 0; k <= i; k++) {
					V[k][i + 1] = 0.0;
				}
			}
			for(int j = 0; j < n; j++) {
				d[j] = V[n - 1][j];
				V[n - 1][j] = 0.0;
			}
			V[n - 1][n - 1] = 1.0;
			e[0] = 0.0;
		}

		// Symmetric tridiagonal QL algorithm.

		private void tql2() {
			//  This is derived from the Algol procedures tql2, by
			//  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
			//  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
			//  Fortran subroutine in EISPACK.

			for(int i = 1; i < n; i++) {
				e[i - 1] = e[i];
			}
			e[n - 1] = 0.0;

			double f = 0.0;
			double tst1 = 0.0;
			double eps = Math.Pow(2.0, - 52.0);
			for(int l = 0; l < n; l++) {
				// Find small subdiagonal element

				tst1 = Math.Max(tst1, Math.Abs(d[l]) + Math.Abs(e[l]));
				int m = l;
				while(m < n) {
					if(Math.Abs(e[m]) <= eps*tst1) {
						break;
					}
					m++;
				}

				// If m == l, d[l] is an eigenvalue,
				// otherwise, iterate.

				if(m > l) {
					int iter = 0;
					do {
						iter = iter + 1; // (Could check iteration count here.)

						// Compute implicit shift

						double g = d[l];
						double p = (d[l + 1] - g)/(2.0*e[l]);
						double r = Maths.Hypot(p, 1.0);
						if(p < 0) {
							r = - r;
						}
						d[l] = e[l]/(p + r);
						d[l + 1] = e[l]*(p + r);
						double dl1 = d[l + 1];
						double h = g - d[l];
						for(int i = l + 2; i < n; i++) {
							d[i] -= h;
						}
						f = f + h;

						// Implicit QL transformation.

						p = d[m];
						double c = 1.0;
						double c2 = c;
						double c3 = c;
						double el1 = e[l + 1];
						double s = 0.0;
						double s2 = 0.0;
						for(int i = m - 1; i >= l; i--) {
							c3 = c2;
							c2 = c;
							s2 = s;
							g = c*e[i];
							h = c*p;
							r = Maths.Hypot(p, e[i]);
							e[i + 1] = s*r;
							s = e[i]/r;
							c = p/r;
							p = c*d[i] - s*g;
							d[i + 1] = h + s*(c*g + s*d[i]);

							// Accumulate transformation.

							for(int k = 0; k < n; k++) {
								h = V[k][i + 1];
								V[k][i + 1] = s*V[k][i] + c*h;
								V[k][i] = c*V[k][i] - s*h;
							}
						}
						p = (- s)*s2*c3*el1*e[l]/dl1;
						e[l] = s*p;
						d[l] = c*p;

						// Check for convergence.
					} while(Math.Abs(e[l]) > eps*tst1);
				}
				d[l] = d[l] + f;
				e[l] = 0.0;
			}

			// Sort eigenvalues and corresponding vectors.

			for(int i = 0; i < n - 1; i++) {
				int k = i;
				double p = d[i];
				for(int j = i + 1; j < n; j++) {
					if(d[j] < p) {
						k = j;
						p = d[j];
					}
				}
				if(k != i) {
					d[k] = d[i];
					d[i] = p;
					for(int j = 0; j < n; j++) {
						p = V[j][i];
						V[j][i] = V[j][k];
						V[j][k] = p;
					}
				}
			}
		}

		// Nonsymmetric reduction to Hessenberg form.

		private void orthes() {
			//  This is derived from the Algol procedures orthes and ortran,
			//  by Martin and Wilkinson, Handbook for Auto. Comp.,
			//  Vol.ii-Linear Algebra, and the corresponding
			//  Fortran subroutines in EISPACK.

			int low = 0;
			int high = n - 1;

			for(int m = low + 1; m <= high - 1; m++) {
				// Scale column.

				double scale = 0.0;
				for(int i = m; i <= high; i++) {
					scale = scale + Math.Abs(H[i][m - 1]);
				}
				if(scale != 0.0) {
					// Compute Householder transformation.

					double h = 0.0;
					for(int i = high; i >= m; i--) {
						ort[i] = H[i][m - 1]/scale;
						h += ort[i]*ort[i];
					}
					double g = Math.Sqrt(h);
					if(ort[m] > 0) {
						g = - g;
					}
					h = h - ort[m]*g;
					ort[m] = ort[m] - g;

					// Apply Householder similarity transformation
					// H = (I-u*u'/h)*H*(I-u*u')/h)

					for(int j = m; j < n; j++) {
						double f = 0.0;
						for(int i = high; i >= m; i--) {
							f += ort[i]*H[i][j];
						}
						f = f/h;
						for(int i = m; i <= high; i++) {
							H[i][j] -= f*ort[i];
						}
					}

					for(int i = 0; i <= high; i++) {
						double f = 0.0;
						for(int j = high; j >= m; j--) {
							f += ort[j]*H[i][j];
						}
						f = f/h;
						for(int j = m; j <= high; j++) {
							H[i][j] -= f*ort[j];
						}
					}
					ort[m] = scale*ort[m];
					H[m][m - 1] = scale*g;
				}
			}

			// Accumulate transformations (Algol's ortran).

			for(int i = 0; i < n; i++) {
				for(int j = 0; j < n; j++) {
					V[i][j] = (i == j ? 1.0 : 0.0);
				}
			}

			for(int m = high - 1; m >= low + 1; m--) {
				if(H[m][m - 1] != 0.0) {
					for(int i = m + 1; i <= high; i++) {
						ort[i] = H[i][m - 1];
					}
					for(int j = m; j <= high; j++) {
						double g = 0.0;
						for(int i = m; i <= high; i++) {
							g += ort[i]*V[i][j];
						}
						// Double division avoids possible underflow
						g = (g/ort[m])/H[m][m - 1];
						for(int i = m; i <= high; i++) {
							V[i][j] += g*ort[i];
						}
					}
				}
			}
		}

		// Complex scalar division.

		private void cdiv(double xr, double xi, double yr, double yi) {
			double r, d;
			if(Math.Abs(yr) > Math.Abs(yi)) {
				r = yi/yr;
				d = yr + r*yi;
				cdivr = (xr + r*xi)/d;
				cdivi = (xi - r*xr)/d;
			} else {
				r = yr/yi;
				d = yi + r*yr;
				cdivr = (r*xr + xi)/d;
				cdivi = (r*xi - xr)/d;
			}
		}

		// Nonsymmetric reduction from Hessenberg to real Schur form.

		private void hqr2() {
			//  This is derived from the Algol procedure hqr2,
			//  by Martin and Wilkinson, Handbook for Auto. Comp.,
			//  Vol.ii-Linear Algebra, and the corresponding
			//  Fortran subroutine in EISPACK.

			// Initialize

			int nn = this.n;
			int n = nn - 1;
			int low = 0;
			int high = nn - 1;
			double eps = Math.Pow(2.0, - 52.0);
			double exshift = 0.0;
			double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;

			// Store roots isolated by balanc and compute matrix norm

			double norm = 0.0;
			for(int i = 0; i < nn; i++) {
				if(i < low | i > high) {
					d[i] = H[i][i];
					e[i] = 0.0;
				}
				for(int j = Math.Max(i - 1, 0); j < nn; j++) {
					norm = norm + Math.Abs(H[i][j]);
				}
			}

			// Outer loop over eigenvalue index

			int iter = 0;
			while(n >= low) {
				// Look for single small sub-diagonal element

				int l = n;
				while(l > low) {
					s = Math.Abs(H[l - 1][l - 1]) + Math.Abs(H[l][l]);
					if(s == 0.0) {
						s = norm;
					}
					if(Math.Abs(H[l][l - 1]) < eps*s) {
						break;
					}
					l--;
				}

				// Check for convergence
				// One root found

				if(l == n) {
					H[n][n] = H[n][n] + exshift;
					d[n] = H[n][n];
					e[n] = 0.0;
					n--;
					iter = 0;

					// Two roots found
				} else if(l == n - 1) {
					w = H[n][n - 1]*H[n - 1][n];
					p = (H[n - 1][n - 1] - H[n][n])/2.0;
					q = p*p + w;
					z = Math.Sqrt(Math.Abs(q));
					H[n][n] = H[n][n] + exshift;
					H[n - 1][n - 1] = H[n - 1][n - 1] + exshift;
					x = H[n][n];

					// Real pair

					if(q >= 0) {
						if(p >= 0) {
							z = p + z;
						} else {
							z = p - z;
						}
						d[n - 1] = x + z;
						d[n] = d[n - 1];
						if(z != 0.0) {
							d[n] = x - w/z;
						}
						e[n - 1] = 0.0;
						e[n] = 0.0;
						x = H[n][n - 1];
						s = Math.Abs(x) + Math.Abs(z);
						p = x/s;
						q = z/s;
						r = Math.Sqrt(p*p + q*q);
						p = p/r;
						q = q/r;

						// Row modification

						for(int j = n - 1; j < nn; j++) {
							z = H[n - 1][j];
							H[n - 1][j] = q*z + p*H[n][j];
							H[n][j] = q*H[n][j] - p*z;
						}

						// Column modification

						for(int i = 0; i <= n; i++) {
							z = H[i][n - 1];
							H[i][n - 1] = q*z + p*H[i][n];
							H[i][n] = q*H[i][n] - p*z;
						}

						// Accumulate transformations

						for(int i = low; i <= high; i++) {
							z = V[i][n - 1];
							V[i][n - 1] = q*z + p*V[i][n];
							V[i][n] = q*V[i][n] - p*z;
						}

						// Complex pair
					} else {
						d[n - 1] = x + p;
						d[n] = x + p;
						e[n - 1] = z;
						e[n] = - z;
					}
					n = n - 2;
					iter = 0;

					// No convergence yet
				} else {
					// Form shift

					x = H[n][n];
					y = 0.0;
					w = 0.0;
					if(l < n) {
						y = H[n - 1][n - 1];
						w = H[n][n - 1]*H[n - 1][n];
					}

					// Wilkinson's original ad hoc shift

					if(iter == 10) {
						exshift += x;
						for(int i = low; i <= n; i++) {
							H[i][i] -= x;
						}
						s = Math.Abs(H[n][n - 1]) + Math.Abs(H[n - 1][n - 2]);
						x = y = 0.75*s;
						w = (- 0.4375)*s*s;
					}

					// MATLAB's new ad hoc shift

					if(iter == 30) {
						s = (y - x)/2.0;
						s = s*s + w;
						if(s > 0) {
							s = Math.Sqrt(s);
							if(y < x) {
								s = - s;
							}
							s = x - w/((y - x)/2.0 + s);
							for(int i = low; i <= n; i++) {
								H[i][i] -= s;
							}
							exshift += s;
							x = y = w = 0.964;
						}
					}

					iter = iter + 1; // (Could check iteration count here.)

					// Look for two consecutive small sub-diagonal elements

					int m = n - 2;
					while(m >= l) {
						z = H[m][m];
						r = x - z;
						s = y - z;
						p = (r*s - w)/H[m + 1][m] + H[m][m + 1];
						q = H[m + 1][m + 1] - z - r - s;
						r = H[m + 2][m + 1];
						s = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
						p = p/s;
						q = q/s;
						r = r/s;
						if(m == l) {
							break;
						}
						if(Math.Abs(H[m][m - 1])*(Math.Abs(q) + Math.Abs(r)) <
						   eps*(Math.Abs(p)*(Math.Abs(H[m - 1][m - 1]) + Math.Abs(z) + Math.Abs(H[m + 1][m + 1])))) {
							break;
						}
						m--;
					}

					for(int i = m + 2; i <= n; i++) {
						H[i][i - 2] = 0.0;
						if(i > m + 2) {
							H[i][i - 3] = 0.0;
						}
					}

					// Double QR step involving rows l:n and columns m:n

					for(int k = m; k <= n - 1; k++) {
						bool notlast = (k != n - 1);
						if(k != m) {
							p = H[k][k - 1];
							q = H[k + 1][k - 1];
							r = (notlast ? H[k + 2][k - 1] : 0.0);
							x = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
							if(x != 0.0) {
								p = p/x;
								q = q/x;
								r = r/x;
							}
						}
						if(x == 0.0) {
							break;
						}
						s = Math.Sqrt(p*p + q*q + r*r);
						if(p < 0) {
							s = - s;
						}
						if(s != 0) {
							if(k != m) {
								H[k][k - 1] = (- s)*x;
							} else if(l != m) {
								H[k][k - 1] = - H[k][k - 1];
							}
							p = p + s;
							x = p/s;
							y = q/s;
							z = r/s;
							q = q/p;
							r = r/p;

							// Row modification

							for(int j = k; j < nn; j++) {
								p = H[k][j] + q*H[k + 1][j];
								if(notlast) {
									p = p + r*H[k + 2][j];
									H[k + 2][j] = H[k + 2][j] - p*z;
								}
								H[k][j] = H[k][j] - p*x;
								H[k + 1][j] = H[k + 1][j] - p*y;
							}

							// Column modification

							for(int i = 0; i <= Math.Min(n, k + 3); i++) {
								p = x*H[i][k] + y*H[i][k + 1];
								if(notlast) {
									p = p + z*H[i][k + 2];
									H[i][k + 2] = H[i][k + 2] - p*r;
								}
								H[i][k] = H[i][k] - p;
								H[i][k + 1] = H[i][k + 1] - p*q;
							}

							// Accumulate transformations

							for(int i = low; i <= high; i++) {
								p = x*V[i][k] + y*V[i][k + 1];
								if(notlast) {
									p = p + z*V[i][k + 2];
									V[i][k + 2] = V[i][k + 2] - p*r;
								}
								V[i][k] = V[i][k] - p;
								V[i][k + 1] = V[i][k + 1] - p*q;
							}
						} // (s != 0)
					} // k loop
				} // check convergence
			} // while (n >= low)

			// Backsubstitute to find vectors of upper triangular form

			if(norm == 0.0) {
				return;
			}

			for(n = nn - 1; n >= 0; n--) {
				p = d[n];
				q = e[n];

				// Real vector

				if(q == 0) {
					int l = n;
					H[n][n] = 1.0;
					for(int i = n - 1; i >= 0; i--) {
						w = H[i][i] - p;
						r = 0.0;
						for(int j = l; j <= n; j++) {
							r = r + H[i][j]*H[j][n];
						}
						if(e[i] < 0.0) {
							z = w;
							s = r;
						} else {
							l = i;
							if(e[i] == 0.0) {
								if(w != 0.0) {
									H[i][n] = (- r)/w;
								} else {
									H[i][n] = (- r)/(eps*norm);
								}

								// Solve real equations
							} else {
								x = H[i][i + 1];
								y = H[i + 1][i];
								q = (d[i] - p)*(d[i] - p) + e[i]*e[i];
								t = (x*s - z*r)/q;
								H[i][n] = t;
								if(Math.Abs(x) > Math.Abs(z)) {
									H[i + 1][n] = (- r - w*t)/x;
								} else {
									H[i + 1][n] = (- s - y*t)/z;
								}
							}

							// Overflow control

							t = Math.Abs(H[i][n]);
							if((eps*t)*t > 1) {
								for(int j = i; j <= n; j++) {
									H[j][n] = H[j][n]/t;
								}
							}
						}
					}

					// Complex vector
				} else if(q < 0) {
					int l = n - 1;

					// Last vector component imaginary so matrix is triangular

					if(Math.Abs(H[n][n - 1]) > Math.Abs(H[n - 1][n])) {
						H[n - 1][n - 1] = q/H[n][n - 1];
						H[n - 1][n] = (- (H[n][n] - p))/H[n][n - 1];
					} else {
						cdiv(0.0, - H[n - 1][n], H[n - 1][n - 1] - p, q);
						H[n - 1][n - 1] = cdivr;
						H[n - 1][n] = cdivi;
					}
					H[n][n - 1] = 0.0;
					H[n][n] = 1.0;
					for(int i = n - 2; i >= 0; i--) {
						double ra, sa, vr, vi;
						ra = 0.0;
						sa = 0.0;
						for(int j = l; j <= n; j++) {
							ra = ra + H[i][j]*H[j][n - 1];
							sa = sa + H[i][j]*H[j][n];
						}
						w = H[i][i] - p;

						if(e[i] < 0.0) {
							z = w;
							r = ra;
							s = sa;
						} else {
							l = i;
							if(e[i] == 0) {
								cdiv(- ra, - sa, w, q);
								H[i][n - 1] = cdivr;
								H[i][n] = cdivi;
							} else {
								// Solve complex equations

								x = H[i][i + 1];
								y = H[i + 1][i];
								vr = (d[i] - p)*(d[i] - p) + e[i]*e[i] - q*q;
								vi = (d[i] - p)*2.0*q;
								if(vr == 0.0 & vi == 0.0) {
									vr = eps*norm*(Math.Abs(w) + Math.Abs(q) + Math.Abs(x) + Math.Abs(y) + Math.Abs(z));
								}
								cdiv(x*r - z*ra + q*sa, x*s - z*sa - q*ra, vr, vi);
								H[i][n - 1] = cdivr;
								H[i][n] = cdivi;
								if(Math.Abs(x) > (Math.Abs(z) + Math.Abs(q))) {
									H[i + 1][n - 1] = (- ra - w*H[i][n - 1] + q*H[i][n])/x;
									H[i + 1][n] = (- sa - w*H[i][n] - q*H[i][n - 1])/x;
								} else {
									cdiv(- r - y*H[i][n - 1], - s - y*H[i][n], z, q);
									H[i + 1][n - 1] = cdivr;
									H[i + 1][n] = cdivi;
								}
							}

							// Overflow control

							t = Math.Max(Math.Abs(H[i][n - 1]), Math.Abs(H[i][n]));
							if((eps*t)*t > 1) {
								for(int j = i; j <= n; j++) {
									H[j][n - 1] = H[j][n - 1]/t;
									H[j][n] = H[j][n]/t;
								}
							}
						}
					}
				}
			}

			// Vectors of isolated roots

			for(int i = 0; i < nn; i++) {
				if(i < low | i > high) {
					for(int j = i; j < nn; j++) {
						V[i][j] = H[i][j];
					}
				}
			}

			// Back transformation to get eigenvectors of original matrix

			for(int j = nn - 1; j >= low; j--) {
				for(int i = low; i <= high; i++) {
					z = 0.0;
					for(int k = low; k <= Math.Min(j, high); k++) {
						z = z + V[i][k]*H[k][j];
					}
					V[i][j] = z;
				}
			}
		}

		#endregion //  Private Methods

		#region Constructor

		/// <summary>Check for symmetry, then construct the eigenvalue decomposition</summary>
		/// <param name="Arg">   Square matrix
		/// </param>
		/// <returns>     Structure to access D and V.
		/// </returns>
		public EigenvalueDecomposition(Matrix Arg) {
			var A = Arg.Array;
			n = Arg.ColumnDimension;
			V = new double[n][];
			for(int i = 0; i < n; i++) {
				V[i] = new double[n];
			}
			d = new double[n];
			e = new double[n];

			issymmetric = true;
			for(int j = 0; (j < n) & issymmetric; j++) {
				for(int i = 0; (i < n) & issymmetric; i++) {
					issymmetric = (A[i][j] == A[j][i]);
				}
			}

			if(issymmetric) {
				for(int i = 0; i < n; i++) {
					for(int j = 0; j < n; j++) {
						V[i][j] = A[i][j];
					}
				}

				// Tridiagonalize.
				tred2();

				// Diagonalize.
				tql2();
			} else {
				H = new double[n][];
				for(int i2 = 0; i2 < n; i2++) {
					H[i2] = new double[n];
				}
				ort = new double[n];

				for(int j = 0; j < n; j++) {
					for(int i = 0; i < n; i++) {
						H[i][j] = A[i][j];
					}
				}

				// Reduce to Hessenberg form.
				orthes();

				// Reduce Hessenberg to real Schur form.
				hqr2();
			}
		}

		#endregion //  Constructor

		#region Public Properties

		/// <summary>Return the real parts of the eigenvalues</summary>
		/// <returns>     real(diag(D))
		/// </returns>
		public virtual double[] RealEigenvalues {
			get { return d; }
		}

		/// <summary>Return the imaginary parts of the eigenvalues</summary>
		/// <returns>     imag(diag(D))
		/// </returns>
		public virtual double[] ImagEigenvalues {
			get { return e; }
		}

		/// <summary>Return the block diagonal eigenvalue matrix</summary>
		/// <returns>     D
		/// </returns>
		public virtual Matrix D {
			get {
				var X = new Matrix(n, n);
				var D = X.Array;
				for(int i = 0; i < n; i++) {
					for(int j = 0; j < n; j++) {
						D[i][j] = 0.0;
					}
					D[i][i] = d[i];
					if(e[i] > 0) {
						D[i][i + 1] = e[i];
					} else if(e[i] < 0) {
						D[i][i - 1] = e[i];
					}
				}
				return X;
			}
		}

		#endregion //  Public Properties

		#region Public Methods

		/// <summary>Return the eigenvector matrix</summary>
		/// <returns>     V
		/// </returns>
		public virtual Matrix GetVectors() {
			return new Matrix(V, n, n);
		}

		#endregion //  Public Methods

		// A method called when serializing this class.

		#region ISerializable Members

		void ISerializable.GetObjectData(SerializationInfo info, StreamingContext context) {}

		#endregion
	}
}
